Generating numerical algorithms using a computer algebra system

Derivation of Numerical Methods Using Computer Algebra

The use of computer algebra systems in a course on scientific computation is demonstrated. Various examples, such as the derivation of Newton’s iteration formula, the secant method, Newton–Cotes and Gaussian integration formulas, as well as Runge–Kutta formulas, are presented. For the derivations, the computer algebra system Maple is used.

Algorithms for computer algebra

Computer Algebra Algorithms*

INTRODUCTION ...................................................................................................................... 1 ARITHMETIC ........................................................................................................................... 2 Integer and Polynomial Addition, Multiplication, and Division with Remainder ............. 2 Integer and Polynomial Greatest C...

A Computer Algebra System

Systems of polynomial equations appear throughout mathematics, science, and engineering, but solving them is widely considered to be part of numerical analysis, not computer algebra or algebraic geometry. Due to rounding errors, though, purely numerical methods often are unstable in unpredictable ways. They usually don’t find all solutions and frequently have problems with overdetermined system...

Using Computer Algebra to Choose and Apply Numerical Routines

In applied mathematics, electronic and chemical engineering, the modelling process can produce a number of mathematical problems which require numerical solutions for which symbolic methods are either not possible or not obvious. With the plethora of numerical library routines for the solution of these problems often the numerical analyst has to answer the question Which routine to choose? and ...